WASHINGTON — Enrollment in the federal health insurance exchange surged in December, with almost half of the 975,000 signing up in the days before a Dec. 24 deadline.

The new numbers, announced by the administrator for the Centers for Medicare and Medicaid Services in a Sunday blog post, bring to 1.1 million the number of Americans who have enrolled through the exchange since it opened Oct. 1.

"As we continue our open enrollment campaign, we experienced a welcome surge in enrollment as millions of Americans seek access to affordable health care coverage," wrote CMS Administrator Marilyn Tavenner.

Average daily enrollments have gone from less than 1,000 in October to 3,800 in November to 40,000 in December. And as the deadline approached, sign-ups were closer to 100,000 a day.

Tavenner credited improvements in the federal HealthCare.gov website, which was plagued by technical problems from the time it launched Oct. 1 through late November.

As a result of those outages and glitches, the Obama administration twice pushed back the deadline under the 2010 Affordable Care Act — first to Dec. 23 and then to Dec. 24 — to sign up for insurance in order for it to take effect Jan. 1. Major insurers have also extended the deadline for paying premiums on those policies until Jan. 10.

One sign the site is working better, Tavenner wrote, is that 83,000 people were using the site at the same time on Dec. 23. That's far more than the original number federal officials cited Nov. 30, when they announced the site had been fixed.

The federal exchange sign-ups are just one metric of the health care law's success, however. The administration has yet to provide a December update on the 14 states running their own exchanges. While California, New York, Washington, Kentucky and Connecticut have performed well, others are still struggling.

Potentially millions of Americans have had their existing insurance plans canceled because the plans failed to meet the minimum standards under the law. Earlier this month, White House officials said only 500,000 people who had their insurance canceled had not obtained new coverage.

The numbers fall short of administration projections that more than 3.3 million would be enrolled through federal and state exchanges by the end of the year. And unless the administration can sustain the rate of sign-ups in the days before Christmas, it will also fail to meet the goal of 7 million it said would buy insurance before the March 31, 2014, deadline in order to avoid a 2015 tax penalty.

That's important because the law depends on young and relatively healthy people to pay premiums in order to subsidize expensive health care for older Americans.

"We are in the middle of a sustained, six-month open enrollment period that we expect to see enrollment ramp up over time, much like other historic implementation efforts we've seen in Massachusetts and Medicare Part D," Tavenner wrote.